Development of an (Adaptive) Unstructured 2-D Inverse Design Method for Turbomachinery Blades

2002 ◽  
Author(s):  
Benjamin M. F. Choo ◽  
Mehrdad Zangeneh
Keyword(s):  
Shock Waves ◽  
Design Method ◽  
Inverse Design ◽  
Pressure Jump ◽  
Triangular Meshes ◽  
Pressure Loading ◽  
Trailing Edge ◽  
Turbomachinery Blades ◽  
Inverse Design Method ◽  
Blade Geometry

An aerodynamics inverse design method for turbomachinery blades using fully (adaptive) unstructured meshes is presented. In this design method, the pressure loading (i.e. pressure jump across the blades) and thickness distribution are prescribed. The design method then computes the blade shape that would accomplish this loading. This inverse design method is implemented using a cell-centred finite volume method which solves the Euler equations on Delaunay unstructured triangular meshes using upwind flux vector splitting scheme. The analysis/direct Euler solver first is validated against some test cases of cascades flow. Computational grid and solution adaptation is performed to capture any flow behaviors such as shock waves using some error indicators. In the inverse design method, blade geometry is updated at the end of each design iteration process. A flexible and fast remeshing process based on a classical ‘spring’ methodology is adopted. An improved spring smoothing methodology for large changes of blades geometry is also presented. This flexible remeshing method can be used in designing a real blade (i.e. round leading and trailing edge) and also ‘fat’ turbine blades with blunt leading and trailing edge. The inverse design method using unstructured triangular meshes is validated by regeneration of a generic compressor rotor blade geometry subjected to a specified pressure loading and blade thickness. Finally, the method is applied to the design of the tip section of Nasa Rotor 67. The result shows that the design method is very useful in controlling shock waves.

Multi-Objective Optimization of a High Specific Speed Centrifugal Volute Pump Using Three-Dimensional Inverse Design Coupled With Computational Fluid Dynamics Simulations

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Luying Zhang ◽  
Gabriel Davila ◽  
Mehrdad Zangeneh
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Design Method ◽  
Three Dimensional ◽  
Inverse Design ◽  
Computational Time ◽  
Specific Speed ◽  
Meridional Shape ◽  
Inverse Design Method ◽  
Blade Geometry

Abstract This paper presents three different multiobjective optimization strategies for a high specific speed centrifugal volute pump design. The objectives of the optimization consist of maximizing the efficiency and minimizing the cavitation while maintaining the Euler head. The first two optimization strategies use a three-dimensional (3D) inverse design method to parametrize the blade geometry. Both meridional shape and 3D blade geometry are changed during the optimization. In the first approach, design of experiment (DOE) method is used and the pump efficiency is obtained from computational fluid dynamics (CFD) simulations, while cavitation is evaluated by using minimum pressure on blade surface predicted by 3D inverse design method. The design matrix is then used to create a surrogate model where optimization is run to find the best tradeoff between cavitation and efficiency. This optimized geometry is manufactured and tested and is found to be 3.9% more efficient than the baseline with reduced cavitation at high flow. In the second approach, only the 3D inverse design method output is used to compute the efficiency and cavitation parameters and this leads to considerable reduction to the computational time. The resulting optimized geometry is found to be similar to the computationally more expensive solution based on 3D CFD results. In order to compare the inverse design based optimization to the conventional optimization, an equivalent optimization is carried out by parametrizing the blade angle and meridional shape.

Design of a Propeller Fan Using 3-D Inverse Design Method and CFD for High Efficiency and Low Aerodynamic Noise

2009 ◽  
Author(s):  
Hidenobu Okamoto ◽  
Akira Goto ◽  
Masato Furukawa
Keyword(s):  
High Efficiency ◽  
Design Method ◽  
Selective Laser Sintering ◽  
Design Guidelines ◽  
Low Noise ◽  
Inverse Design ◽  
Aerodynamic Noise ◽  
Pressure Jump ◽  
Blade Loading ◽  
Inverse Design Method

Three-Dimensional Inverse Design Method, where the 3-D blade profile is designed for a specified blade loading distribution, has been applied for designing a propeller fan rotor with high efficiency and low noise. A variety of the blade loading distributions (pressure jump across the blade), vortex pattern (forced vortex, free vortex, and compound vortex) and the stacking conditions (sweep angles) were specified and the corresponding 3-D blade configurations were obtained. Among the 22 different designs, 14 propeller fan rotors including the reproduced baseline fan were manufactured by a rapid prototyping based on a selective laser sintering system (SLS) and tested. It was confirmed experimentally that the best design achieved about 5.7 points improvement in the peak total-to-static efficiency and the 2.6dB(A) reduction in aerodynamic noise. The flow mechanisms leading to the higher efficiency and lower aerodynamic noise were discussed based on experiments and the RANS steady flow simulations. Based on these investigations, design guidelines for the inverse design of propeller fan rotors with higher efficiency and lower aerodynamic noise were proposed.

Design of the Blade Geometry of Swept Transonic Fans by 3D Inverse Design

2003 ◽  
Author(s):  
H. Watanabe ◽  
M. Zangeneh
Keyword(s):  
Inverse Method ◽  
Design Method ◽  
Pressure Ratio ◽  
Inverse Design ◽  
Specific Work ◽  
Design Practice ◽  
Blade Loading ◽  
Inverse Design Method ◽  
Transonic Fan ◽  
Blade Geometry

The application of sweep in the design of transonic fans has been shown to be an effective method of controlling the strength and position of the shock wave at the tip of transonic fan rotors, and the control of corner separations in stators. In rotors sweep can extend the range significantly. However, using sweep in conventional design practice can also result in a change in specific work and therefore pressure ratio. As a result, laborious iterations are required in order to recover the correct specific work and pressure ratio. In this paper, the blade geometry of a transonic fan is designed with sweep using a 3D inverse design method in which the blade geometry is computed for a specified distribution of blade loading. By comparing the resulting flow field in the conventionally and inversely designed swept rotors, it is shown that it is possible to apply sweep without the need to iterate to maintain pressure ratio and specific work when using the inverse method.

On Design of Transonic Fan Rotors by 3D Inverse Design Method

2006 ◽  
Author(s):  
Peixin Hu ◽  
Mehrdad Zangeneh ◽  
Benjamin Choo ◽  
Mohammad Rahmati
Keyword(s):  
Structural Integrity ◽  
Design Method ◽  
Leading Edge ◽  
Tip Clearance ◽  
Inverse Design ◽  
Pressure Loading ◽  
Tip Clearance Flow ◽  
Blade Thickness ◽  
Inverse Design Method ◽  
Transonic Fan

The application of 3D inverse design to transonic fans can offer designers many advantages in terms of reduction in design time and providing a more direct means of using the insight obtained into flow physics from CFD computations directly in the design process. A number of papers on application of inverse design method to transonic fans have already been reported. However, in order to apply this approach in product design a number of issues need to be addressed. For example, how can the method be used to affect and control the fan rotor characteristics? The robustness of the method and its ability to deal with accurate representation of leading and trailing edges, as well as tip clearance flow. In this paper the further enhancement of the 3D viscous transonic inverse design code TURBOdesign-2 and its application to the re-design of NASA37 and NASA67 rotors will be described. In this inverse design method the blade geometry can be computed by the specification of the blade loading (meridional derivative of rVθ) or the pressure loading. In both cases the blade normal thickness is specified to ensure structural integrity of the design. Improvements to the code include implementation of full approximation storage (FAS) multigrid technique in the solver, which increases the speed of the computation. This method allows the modification of blade thickness and pressure loading by B-splines. In addition improvements have been made in the treatment of proper leading edge geometry. Two well known examples of NASA 67 and NASA 37 rotors are used to provide a step-by-step guide to the application of the method to the design of transonic fan rotors. Improved designs are validated by commercial CFD code CFX.

scholarly journals A Viscous Transonic Inverse Design Method for Turbomachinery Blades: Part I — 2D Cascades

1998 ◽  
Author(s):  
W. T. Tiow ◽  
M. Zangeneh
Keyword(s):  
Thickness Distribution ◽  
Inverse Design ◽  
Specific Work ◽  
Normal Velocity ◽  
Pressure Loading ◽  
Blade Shape ◽  
Turbomachinery Blades ◽  
Stator Blade ◽  
The Difference ◽  
Blade Geometry

An inverse design methodology is presented for the design of turbomachinery blades using a cell-vertex finite volume time-marching algorithm in transonic viscous flow. In this method the blade shape is designed subject to a specified distribution of pressure loading (the difference in pressure across the blade) and thickness distribution. The difference between specified pressure loading and the pressures on the initial blade shape results in a normal velocity through the blade, which is then used to update the blade shapes. Viscous effects are represented by using a distributed body force. A simple and fast iterative scheme is proposed for automatically finding a suitable pressure loading that will provide a specified flow turning (or specific work). The method, therefore, can be applied to the design of new blade geometry without any need to supply information on the initial blade geometry or the blade loading corresponding to an existing design. The Euler solver is first validated by using experimental data for a turbine stage. The accuracy of the inverse procedure is then verified by designing the stator blade from the computed pressure loading. Finally the method is applied to the design of an axial transonic turbine stator and an axial compressor rotor and stator blade.

Redesign of a Low Speed Turbine Stage Using a New Viscous Inverse Design Method

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Benedikt Roidl ◽  
Wahid Ghaly
Keyword(s):  
Stokes Equations ◽  
Design Method ◽  
Accurate Solution ◽  
Inverse Design ◽  
Pressure Loading ◽  
Turbine Stage ◽  
Low Speed ◽  
Target Pressure ◽  
Stage Performance ◽  
Inverse Design Method

The midspan section of a low speed subsonic turbine stage that is built and tested at DFVLR, Cologne, is redesigned using a new inverse blade design method, where the blade walls move with a virtual velocity distribution derived from the difference between the current and target pressure distributions on the blade surfaces. This new inverse method is fully consistent with the viscous flow assumption and is implemented into the time-accurate solution of the Reynolds-averaged Navier–Stokes equations. An algebraic Baldwin–Lomax turbulence model is used for turbulence closure. The mixing plane approach is used to couple the stator and rotor regions. The computational fluid dynamics (CFD) analysis formulation is first assessed against the turbine stage experimental data. The inverse formulation that is implemented in the same CFD code is assessed for its robustness and merits. The inverse design method is then used to study the effect of the rotor pressure loading on the blade shape and stage performance. It is also used to simultaneously redesign both stator and rotor blades for improved stage performance. The results show that by carefully tailoring the target pressure loading on both blade rows, improvement can be achieved in the stage performance.

Redesign of a Low Speed Turbine Stage Using a New Viscous Inverse Design Method

2008 ◽  
Author(s):  
Benedikt Roidl ◽  
Wahid Ghaly
Keyword(s):  
Stokes Equations ◽  
Design Method ◽  
Accurate Solution ◽  
Inverse Design ◽  
Pressure Loading ◽  
Turbine Stage ◽  
Low Speed ◽  
Target Pressure ◽  
Stage Performance ◽  
Inverse Design Method

The midspan section of a low speed subsonic turbine stage that is built and tested at DFVLR, Cologne, is redesigned using a new inverse blade design method where the blade walls move with a virtual velocity distribution derived from the difference between the current and the target pressure distributions on the blade surfaces. This new inverse method is fully consistent with the viscous flow assumption and is implemented into the time accurate solution of the Reynolds-Averaged Navier-Stokes equations. An algebraic Baldwin-Lomax turbulence model is used for turbulence closure. The mixing plane approach is used to couple the stator and the rotor regions. The CFD analysis formulation is first assessed against the turbine stage experimental data. The inverse formulation that is implemented in the same CFD code is also assessed for its robustness and merits. The inverse design method is then used to study the effect of the rotor pressure loading on the blade shape and stage performance. It is also used to simultaneously redesign both stator and rotor blades for improved stage performance. The results show that by carefully tailoring the target pressure loading on both blade rows, improvement can be achieved in the stage performance.

An Iterative Inverse Design Method of Turbomachinery Blades by Using Proper Orthogonal Decomposition

2015 ◽  
Author(s):  
Jiaqi Luo ◽  
Xiao Tang ◽  
Yanhui Duan ◽  
Feng Liu
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Design Methodology ◽  
Design Method ◽  
Aerodynamic Performance ◽  
Orthogonal Decomposition ◽  
Inverse Design ◽  
Turbomachinery Blades ◽  
Inverse Design Method ◽  
Proper Orthogonal ◽  
Gappy Pod

This paper presents an iterative inverse design methodology based on proper orthogonal decomposition (POD) and its applications to the inverse design of turbomachinery blades. In the aerodynamic system with a number of snapshots, the aerodynamic performance with the corresponding aerodynamic shape within the design space can be described as a linear combination of a series of POD basis modes. In the present paper, the description ability of Gappy POD is evaluated firstly and the influence of different parametrization methods and different snapshot approaches are studied and compared in detail. In the POD-based inverse design, the aerodynamic shape can be obtained by only one design process. However, due to the error between the predicted aerodynamic performance by Gappy POD and that obtained from computational fluid dynamics, an iterative inverse design methodology is proposed herein based on the error correction to the target aerodynamic performance. Three inverse design studies of turbomachinery blades are performed. In the first two cases, the profiles of two-dimensional turbine blades are modified to approach the target pressure distributions on the blade surface in subsonic and transonic flow, respectively. In the third case, a three-dimensional supersonic turbine blade is restaggered along span to achieve a given loading distribution in the spanwise direction at the outlet. The design results are presented and compared in detail, demonstrating the effectiveness and improved accuracy of the POD-based iterative inverse design method.

Inviscid-Viscous Interaction Method for 3D Inverse Design of Centrifugal Impellers

1993 ◽  
Author(s):  
M. Zangeneh
Keyword(s):  
Design Method ◽  
Thickness Distribution ◽  
Pressure Ratio ◽  
Inverse Design ◽  
Navier Stokes ◽  
Viscous Effects ◽  
High Pressure Ratio ◽  
Circulation Distribution ◽  
Inverse Design Method ◽  
Blade Geometry

A 3D inverse design method for the design of the blade geometry of centrifugal compressor impellers is presented. In this method the blade shape is computed for a specified circulation distribution, normal (or tangential) thickness distribution and meridional geometry. As the blade shapes are computed by using an inviscid slip (or flow tangency) condition, the viscous effects are introduced indirectly by using a viscous/inviscid procedure. The 3D Navier-Stokes solver developed by Dawes is used as the viscous method. Two different approaches are described for incorporating the viscous effects into the inviscid design method. One method is based on the introduction of an aerodynamic blockage distribution throughout the meridional geometry. While in the other approach a vorticity term directly related to the entropy gradients in the machine is introduced. The method is applied to redesign the blade geometry of Eckardt’s 30° backswept impeller as well as a generic high pressure ratio (transonic) impeller. The results indicate that the entropy gradient approach can fairly accurately represent the viscous effects in the machine.

Redesign of Axial Fan using Viscous Inverse Design Method based on Boundary Vorticity Flux Diagnosis

2021 ◽  
pp. 1-42
Author(s):  
Hui Liu ◽  
Boyan Jiang ◽  
Wei Wang ◽  
Xiaopei Yang ◽  
Jun Wang
Keyword(s):  
Design Method ◽  
Internal Flow ◽  
Inverse Design ◽  
Pressure Loading ◽  
Axial Fan ◽  
High Quality ◽  
Wall Boundary Conditions ◽  
Aerodynamic Parameters ◽  
Inverse Design Method ◽  
Vorticity Flux

Abstract The inverse design method for turbomachinery can directly acquire a blade geometry with specific aerodynamic parameters, such as pressure loading on the blade surfaces. The difference between the inverse design and direct analysis design is that the management of the flow field is controlled by aerodynamic parameters instead of geometric parameters. Although the inverse design has been studied since the 1940s, it is far from being mature enough in comparison with the analysis method. In this work, the inverse problem method is improved by two aspects: the calculation accuracy and the strategy to determine the pressure loading distribution. The application of a high-quality mesh auto-generation and deformation technique to the inverse design is introduced. The no-slip wall boundary conditions, similar to the analysis mode, and high-quality mesh enable the use of an advanced turbulence model in the inverse design. These methods improve the accuracy of the inverse design. The loading distribution in the inverse design is obtained based on the boundary vorticity flux diagnosis. An axial fan is redesigned as an example of the inverse design method. The internal flow loss analysis based on the entropy production theory verifies the effectiveness of the inverse design used in this study.

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